Improved Perturbation Method and its Application to the IIB Matrix Model

We present a new scheme for extracting approximate values in ``the improved perturbation method'', which is a sort of resummation technique capable of evaluating a series outside the radius of convergence. We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the ``plateau'' structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observables separately and be analyzed comprehensively. We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space-time extent. In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)- and SO(7)-symmetric vacua that have been observed. It is also found that there are two distinct SO(4)-symmetric vacua that have almost the same value of free energy but the extent of space-time is different. From the approximate values of free energy, we conclude that the SO(4)-symmetric vacua are most preferred among those three types of vacua.Comment: 52 pages, published versio

On the Definition of the Partition Function in Quantum Regge Calculus

We argue that the definition of the partition function used recently to demonstrate the failure of Regge calculus is wrong. In fact, in the one-dimensional case, we show that there is a more natural definition, with which one can reproduce the correct results.Comment: 9 pages, LaTe

A Failing Grade: "High-Tuition/High-Aid"

In the face of impending budget cuts to higher education, Washington policymakers are considering adopting a "high-tuition/high-aid" model that significantly increases tuition, partly offset with more financial aid. The assumption of this approach is that students who can afford it pay more; those students who cannot, benefit from larger financial aid packages. But the experience of universities that have adopted this model shows that high-tuition/high-aid preserves neither access nor quality

Differential Geometry of Microlinear Frolicher Spaces II

In this paper, as the second in our series of papers on differential geometry of microlinear Frolicher spaces, we study differenital forms. The principal result is that the exterior differentiation is uniquely determined geometrically, just as grad (ient), div (ergence) and rot (ation) are uniquely determined geometrically or physically in classical vector calculus. This infinitesimal characterization of exterior differentiation has been completely missing in orthodox differential geometry